Powers and roots calculator

Calculate the power of a number or extract the root of any power online. A simple and accurate calculator with formulas.

Degrees
6
Roots
99.9%
Calculation accuracy

Powers and roots calculator

Calculate the power of a number or extract the root of any power online. A simple and accurate calculator with formulas.

Calculation parameters

About the powers and roots calculator

Online calculator for calculating powers of numbers and extracting roots of any degree. An easy-to-use tool with automatic calculation using mathematical formulas. Suitable for students, engineers and anyone who needs to quickly calculate the power or root of a number.

Our exponents and roots calculator supports all basic mathematical operations with exponents and roots. Whether you are an algebra student, an engineer working on technical calculations, or just need to calculate the power of a number, this tool provides accurate results instantly.

Examples of calculations

Let's look at various examples of using the powers and roots calculator:

Examples of exponentiation

Squaring
5² = 5 × 5 = 25

The square of 5 is 25

Cube
3³ = 3 × 3 × 3 = 27

The cube of number 3 is 27

Raising to the fourth power
2⁴ = 2 × 2 × 2 × 2 = 16

The number 2 to the fourth power is 16

Raising to a negative power
2⁻³ = 1/(2³) = 1/8 = 0.125

The number 2 to the power -3 is 0.125

Raising to a fractional power
8^(1/3) = ∛8 = 2

The number 8 to the power of 1/3 is 2

Examples of root extraction

Square root
√16 = 4

The square root of 16 is 4, since 4² = 16

Cube root
∛27 = 3

The cube root of 27 is 3 since 3³ = 27

Fourth root
∜81 = 3

The fourth root of 81 is 3, since 3⁴ = 81

Fifth root
∛32 = 2

The fifth root of 32 is 2, since 2⁵ = 32

Decimal root
√0.25 = 0.5

The square root of 0.25 is 0.5, since 0.5² = 0.25

How to use the calculator

Select the calculation mode: exponentiation or root extraction. Enter the required values ​​and click the 'Calculate' button. The calculator will automatically apply the appropriate formula and show the result.

Example of exponentiation

Hopefully:

Calculation: 2 × 2 × 2 = 8

2 to the power of 3 equals 8

Root extraction example

Hopefully: ∛8

Calculation: 2³ = 8, поэтому ∛8 = 2

The cube root of 8 is 2

Benefits of the calculator

Fast and accurate calculations, support for powers and roots of any degree, clear interface, automatic application of mathematical formulas, results accurate to 6 decimal places.

Accurate calculations

Uses up-to-date mathematical formulas and ensures high accuracy of calculations

Flexible settings

Supports powers and roots of any degree, including negative and fractional exponents

Full analysis

Shows formulas, step-by-step solutions and detailed calculation information

Export data

Ability to save results in various formats for future use

Tips for use

Make sure all values ​​are correct. For powers, enter the base and exponent. For roots, enter the number and degree of the root. The result is displayed with high accuracy.

Important Notes:

  • You cannot raise 0 to a negative power
  • You cannot take an even root from a negative number.
  • The degree of the root cannot be 0
  • Results are displayed with an accuracy of 6 decimal places
  • Use decimal notation for accurate calculations

Applications

Mathematics and algebra

  • Solving algebraic equations
  • Geometry calculations
  • Studying functions and graphs
  • Mathematical analysis

Science and Engineering

  • Physical calculations
  • Engineering Computing
  • Statistical analysis
  • Scientific research

Frequently Asked Questions

How to raise a number to a power online?

Select the 'Exponentiation' mode, enter the base and exponent, click 'Calculate'. For example, for 2³, enter base 2 and power 3.

How to extract the root of any degree?

Select the 'Root Extraction' mode, enter the number and degree of the root. For example, for ∛8, enter the number 8 and the root power 3.

Is it possible to raise it to a negative power?

Yes, the calculator supports negative powers. For example, 2⁻³ = 1/(2³) = 0.125.

How to calculate fractional power?

The fractional power is equivalent to taking the root. For example, 8^(1/3) = ∛8 = 2.

What is a square root?

The square root of a is the number that, when squared, gives a. For example, √9 = 3, since 3² = 9.

What is a cube root?

The cube root of a is the number that, when cubed, gives a. For example, ∛8 = 2, since 2³ = 8.

Is it possible to take the root of a negative number?

Only the odd root can be extracted from a negative number. An even root of a negative number does not exist in real numbers.

How does the degree calculator work?

The calculator uses the formula aⁿ = a × a × ... × a (n times). For negative powers, the formula a⁻ⁿ = 1/aⁿ is used.

How does the roots calculator work?

The calculator finds a number x such that xⁿ = a, where a is the radical number, n is the power of the root.

Is it possible to raise 0 to a power?

0 can be raised to any positive power, the result will be 0. 0⁰ is undefined.

What is a degree with exponent 0?

Any number to the power of 0 is equal to 1 (except 0⁰). For example, 5⁰ = 1, 100⁰ = 1.

How to calculate the root of a large number?

The calculator automatically processes numbers of any size. Just enter the number and the degree of the root.

Can decimal numbers be used?

Yes, the calculator supports decimals for both base and power or root.

How to calculate the root of a fraction?

The root of a fraction is equal to the root of the numerator divided by the root of the denominator. For example, √(4/9) = √4/√9 = 2/3.

What are irrational roots?

Irrational roots are roots that cannot be represented as an ordinary fraction. For example, √2 ≈ 1.414.

How to check whether the root is calculated correctly?

Raise the result to the power of the root. If you get the original number, the calculation is correct. For example, ∛8 = 2, check: 2³ = 8.

Is it possible to calculate the root of a power greater than 10?

Yes, the calculator supports roots of any degree, including very large exponents.

How to calculate exponent with decimal exponent?

Exponents with a decimal exponent are calculated using logarithms. The calculator automatically handles such cases.

What is the nth root?

The nth root of a number is a number x such that xⁿ = a. Denoted as ⁿ√a or a^(1/n).

How to calculate the power of a number greater than 100?

The calculator automatically processes numbers of any size. Just enter the base and degree.

Can the calculator be used for scientific calculations?

Yes, the calculator is suitable for scientific and engineering calculations, providing high accuracy of calculations.

How to calculate the root of a product?

The root of a product is equal to the product of the roots. For example, √(a×b) = √a × √b.

What is an arithmetic root?

An arithmetic root is a non-negative root value. For example, √9 = 3 (not -3).

How to calculate the power of a product?

The power of a product is equal to the product of powers. For example, (a×b)ⁿ = aⁿ × bⁿ.

Is it possible to calculate the root of a degree?

Yes, the root of a degree is equal to the degree divided by the degree of the root. For example, √(aⁿ) = a^(n/2).

How to calculate the degree of a root?

The degree of a root is equal to the root raised to a power. For example, (ⁿ√a)ᵐ = ⁿ√(aᵐ).

What are complex roots?

Complex roots appear when you take an even root from a negative number. The calculator shows the real part.

How to calculate the root of a sum?

The root of the sum is not equal to the sum of the roots. For example, √(a+b) ≠ √a + √b.

Can I use a calculator for learning?

Yes, the calculator is great for learning math, showing formulas and step-by-step solutions.

How to calculate the root of a quotient?

The root of the quotient is equal to the quotient of the roots. For example, √(a/b) = √a / √b.